ABCF->ab-angle angle

Average Accuracy: 53.6% → 80.9%

Time: 18.1s

Precision: binary64

Cost: 20164

Math

\[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

↓

\[\begin{array}{l} \mathbf{if}\;C \leq 2.1 \cdot 10^{+165}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)}{\pi}\\ \end{array} \]

FPCore

(FPCore (A B C)
 :precision binary64
 (*
  180.0
  (/
   (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0))))))
   PI)))

↓

(FPCore (A B C)
 :precision binary64
 (if (<= C 2.1e+165)
   (/ (/ (atan (/ (- (- C A) (hypot B (- A C))) B)) 0.005555555555555556) PI)
   (/ (* 180.0 (atan (fma -0.5 (/ B C) (/ (* A 0.0) B)))) PI)))

C

double code(double A, double B, double C) {
	return 180.0 * (atan(((1.0 / B) * ((C - A) - sqrt((pow((A - C), 2.0) + pow(B, 2.0)))))) / ((double) M_PI));
}

↓

double code(double A, double B, double C) {
	double tmp;
	if (C <= 2.1e+165) {
		tmp = (atan((((C - A) - hypot(B, (A - C))) / B)) / 0.005555555555555556) / ((double) M_PI);
	} else {
		tmp = (180.0 * atan(fma(-0.5, (B / C), ((A * 0.0) / B)))) / ((double) M_PI);
	}
	return tmp;
}

Julia

function code(A, B, C)
	return Float64(180.0 * Float64(atan(Float64(Float64(1.0 / B) * Float64(Float64(C - A) - sqrt(Float64((Float64(A - C) ^ 2.0) + (B ^ 2.0)))))) / pi))
end

↓

function code(A, B, C)
	tmp = 0.0
	if (C <= 2.1e+165)
		tmp = Float64(Float64(atan(Float64(Float64(Float64(C - A) - hypot(B, Float64(A - C))) / B)) / 0.005555555555555556) / pi);
	else
		tmp = Float64(Float64(180.0 * atan(fma(-0.5, Float64(B / C), Float64(Float64(A * 0.0) / B)))) / pi);
	end
	return tmp
end

Wolfram

code[A_, B_, C_] := N[(180.0 * N[(N[ArcTan[N[(N[(1.0 / B), $MachinePrecision] * N[(N[(C - A), $MachinePrecision] - N[Sqrt[N[(N[Power[N[(A - C), $MachinePrecision], 2.0], $MachinePrecision] + N[Power[B, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / Pi), $MachinePrecision]), $MachinePrecision]

↓

code[A_, B_, C_] := If[LessEqual[C, 2.1e+165], N[(N[(N[ArcTan[N[(N[(N[(C - A), $MachinePrecision] - N[Sqrt[B ^ 2 + N[(A - C), $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]], $MachinePrecision] / 0.005555555555555556), $MachinePrecision] / Pi), $MachinePrecision], N[(N[(180.0 * N[ArcTan[N[(-0.5 * N[(B / C), $MachinePrecision] + N[(N[(A * 0.0), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / Pi), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if C < 2.1000000000000001e165

   1. Initial program 59.3%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Simplified 75.5%

      \[\leadsto \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)} \]
      Proof

      [Start] 59.3	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 59.3	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      associate-*l/ [<=] 59.3	\[ \color{blue}{\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)} \]
      associate-*l/ [=>] 59.3	\[ \frac{180}{\pi} \cdot \tan^{-1} \color{blue}{\left(\frac{1 \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}{B}\right)} \]

   3. Applied egg-rr 80.8%

      \[\leadsto \color{blue}{\frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{0.005555555555555556}}{\pi}} \]
      Proof

      [Start] 75.5	\[ \frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right) \]
      associate-*l/ [=>] 75.5	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\pi}} \]
      *-un-lft-identity [=>] 75.5	\[ \frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\color{blue}{1 \cdot \pi}} \]
      associate-/r* [=>] 75.5	\[ \color{blue}{\frac{\frac{180 \cdot \tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{1}}{\pi}} \]
      *-commutative [=>] 75.5	\[ \frac{\frac{\color{blue}{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right) \cdot 180}}{1}}{\pi} \]
      associate-/l* [=>] 75.5	\[ \frac{\color{blue}{\frac{\tan^{-1} \left(\frac{C - \left(A + \mathsf{hypot}\left(B, A - C\right)\right)}{B}\right)}{\frac{1}{180}}}}{\pi} \]
      associate--r+ [=>] 80.8	\[ \frac{\frac{\tan^{-1} \left(\frac{\color{blue}{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}}{B}\right)}{\frac{1}{180}}}{\pi} \]
      metadata-eval [=>] 80.8	\[ \frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\color{blue}{0.005555555555555556}}}{\pi} \]

   if 2.1000000000000001e165 < C

   1. Initial program 10.8%

      \[180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]

   2. Simplified 10.8%

      \[\leadsto \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + B \cdot B}\right)\right)}{\pi}} \]
      Proof

      [Start] 10.8	\[ 180 \cdot \frac{\tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi} \]
      associate-*r/ [=>] 10.8	\[ \color{blue}{\frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}{\pi}} \]
      sub-neg [=>] 10.8	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) + \left(-\sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)\right)}\right)}{\pi} \]
      sub-neg [<=] 10.8	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \color{blue}{\left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + {B}^{2}}\right)}\right)}{\pi} \]
      unpow2 [=>] 10.8	\[ \frac{180 \cdot \tan^{-1} \left(\frac{1}{B} \cdot \left(\left(C - A\right) - \sqrt{{\left(A - C\right)}^{2} + \color{blue}{B \cdot B}}\right)\right)}{\pi} \]

   3. Taylor expanded in C around inf 42.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B} + -1 \cdot \frac{A + -1 \cdot A}{B}\right)}}{\pi} \]

   4. Simplified 42.4%

      \[\leadsto \frac{180 \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{A \cdot 0}{B}\right)\right)}}{\pi} \]
      Proof

      [Start] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(-0.5 \cdot \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B} + -1 \cdot \frac{A + -1 \cdot A}{B}\right)}{\pi} \]
      fma-def [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \color{blue}{\left(\mathsf{fma}\left(-0.5, \frac{\left({B}^{2} + {A}^{2}\right) - {\left(-1 \cdot A\right)}^{2}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)}}{\pi} \]
      +-commutative [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{\left({A}^{2} + {B}^{2}\right)} - {\left(-1 \cdot A\right)}^{2}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)}{\pi} \]
      associate--l+ [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{{A}^{2} + \left({B}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)}{\pi} \]
      unpow2 [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{\color{blue}{A \cdot A} + \left({B}^{2} - {\left(-1 \cdot A\right)}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)}{\pi} \]
      unpow2 [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(\color{blue}{B \cdot B} - {\left(-1 \cdot A\right)}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)}{\pi} \]
      mul-1-neg [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\color{blue}{\left(-A\right)}}^{2}\right)}{C \cdot B}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)}{\pi} \]
      *-commutative [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{\color{blue}{B \cdot C}}, -1 \cdot \frac{A + -1 \cdot A}{B}\right)\right)}{\pi} \]
      associate-*r/ [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \color{blue}{\frac{-1 \cdot \left(A + -1 \cdot A\right)}{B}}\right)\right)}{\pi} \]
      distribute-rgt1-in [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{-1 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot A\right)}}{B}\right)\right)}{\pi} \]
      associate-*r* [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{\left(-1 \cdot \left(-1 + 1\right)\right) \cdot A}}{B}\right)\right)}{\pi} \]
      metadata-eval [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\left(-1 \cdot \color{blue}{0}\right) \cdot A}{B}\right)\right)}{\pi} \]
      metadata-eval [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{0} \cdot A}{B}\right)\right)}{\pi} \]
      metadata-eval [<=] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{\left(-1 + 1\right)} \cdot A}{B}\right)\right)}{\pi} \]
      *-commutative [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{\color{blue}{A \cdot \left(-1 + 1\right)}}{B}\right)\right)}{\pi} \]
      metadata-eval [=>] 42.4	\[ \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{A \cdot A + \left(B \cdot B - {\left(-A\right)}^{2}\right)}{B \cdot C}, \frac{A \cdot \color{blue}{0}}{B}\right)\right)}{\pi} \]

   5. Taylor expanded in A around 0 81.9%

      \[\leadsto \frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \color{blue}{\frac{B}{C}}, \frac{A \cdot 0}{B}\right)\right)}{\pi} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;C \leq 2.1 \cdot 10^{+165}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)}{\pi}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	59.7%
Cost	20496

\[\begin{array}{l} t_0 := 180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{if}\;C \leq -3 \cdot 10^{-219}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq -1.15 \cdot 10^{-253}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \mathbf{elif}\;C \leq 4 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;C \leq 5.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{\frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{0.005555555555555556}}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)}{\pi}\\ \end{array} \]

Alternative 2
Accuracy	80.9%
Cost	20164

\[\begin{array}{l} \mathbf{if}\;C \leq 1.15 \cdot 10^{+163}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C - A\right) - \mathsf{hypot}\left(B, A - C\right)}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\mathsf{fma}\left(-0.5, \frac{B}{C}, \frac{A \cdot 0}{B}\right)\right)}{\pi}\\ \end{array} \]

Alternative 3
Accuracy	60.3%
Cost	13832

\[\begin{array}{l} \mathbf{if}\;B \leq 8.2 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.2 \cdot 10^{-209}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{\frac{0.5 \cdot \left(B \cdot B\right)}{A}}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 4
Accuracy	45.5%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq -1.75 \cdot 10^{-65}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{elif}\;B \leq 7.4 \cdot 10^{-174}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 5
Accuracy	50.2%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq 4.8 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-174}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 6
Accuracy	50.2%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq 1.05 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-174}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 7
Accuracy	55.1%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq 4.8 \cdot 10^{-293}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 9.5 \cdot 10^{-187}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 8
Accuracy	55.1%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq 5.4 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 8.2 \cdot 10^{-187}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(0.5 \cdot \frac{B}{A}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 9
Accuracy	55.2%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq 8.2 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 2.9 \cdot 10^{-183}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{0.5}{\frac{A}{B}}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 10
Accuracy	55.1%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq 4.5 \cdot 10^{-296}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{C + B}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 10^{-209}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 11
Accuracy	60.3%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;B \leq 8.5 \cdot 10^{-292}:\\ \;\;\;\;180 \cdot \frac{\tan^{-1} \left(\frac{\left(C + B\right) - A}{B}\right)}{\pi}\\ \mathbf{elif}\;B \leq 7 \cdot 10^{-208}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} \left(\frac{A \cdot 0}{B}\right)}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180}{\pi} \cdot \tan^{-1} \left(\frac{C - B}{B}\right)\\ \end{array} \]

Alternative 12
Accuracy	39.7%
Cost	13188

\[\begin{array}{l} \mathbf{if}\;B \leq -2 \cdot 10^{-311}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} 1}{\pi}\\ \mathbf{else}:\\ \;\;\;\;\frac{180 \cdot \tan^{-1} -1}{\pi}\\ \end{array} \]

Alternative 13
Accuracy	20.8%
Cost	13056

\[\frac{180 \cdot \tan^{-1} -1}{\pi} \]

Reproduce

herbie shell --seed 2023131 
(FPCore (A B C)
  :name "ABCF->ab-angle angle"
  :precision binary64
  (* 180.0 (/ (atan (* (/ 1.0 B) (- (- C A) (sqrt (+ (pow (- A C) 2.0) (pow B 2.0)))))) PI)))